Question

Aflati functiile:
a) f(x-3)= 4x-1

b) f(2x+5)= 3x+1

c) f(2x-x)= x+1

Answer 1

Răspuns:

Explicație pas cu pas:

a) f(x-3)= 4x-1

f(x)=ax+b

f(x-3)=a(x-3) +b

a(x-3) +b=4x-1⇔ ax-3a+ b=4x-1 ⇔ ax=4x si -3a+ b= - 1⇔a=4 si -12+b= - 1

⇔a=4 si b=11⇒f(x)=4x +11

b) f(2x+5)= 3x+1

f(x)=ax+b

f(2x+5)=a(2x+5) +b=3x+1⇔2ax+5a+b=3x+1⇔2ax=3x si 5a +b= -1⇔a=3/2 si

5·3/2 +b=-1 ⇔a=3/2 si b= - 1 - 15/2⇔a=3/2 si b= - 17/2⇒f(x)=3/2x - 17/2

c) f(2x-x)= x+1

f(x)=ax+b

f(2x-x)=x+1⇔f(x)=x+1

Answer 2

a) f(x-3)=4x-1

x-3=y → x=y+3

f(y)=4(y+3)-1=4y+12-1=4y+11

f(x)=4x-11

b) f(2x+5)=3x+1

2x+5=y → x=(y-5):2

f(y)=3(y-5):2+1=(3y-15+2):2=(3y-13):2

f(x)=(3x-13):2

c) f(2x-x)=x+1

f(x)=x+1